3 papers
math.DG2020
The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups
Michael Albanese
Shortly after the introduction of Seiberg-Witten theory, LeBrun showed that the sign of the Yamabe invariant of a compact Kähler surface is determined by its Kodaira dimension. In…
math.AT2019
Connected sums of almost complex manifolds, products of rational homology spheres, and the twisted spin^c Dirac operator
Michael Albanese, Aleksandar Milivojevic
We record an answer to the question "In which dimensions is the connected sum of two closed almost complex manifolds necessarily an almost complex manifold?". In the process of doi…
math.AT2018
On the minimal sum of Betti numbers of an almost complex manifold
Michael Albanese, Aleksandar Milivojevic
We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dime…